Question

Cleo writes down her four favorite numbers. When she takes three of them at a time and

calculates their sum, she gets four possible results: 13, 14, 17 and 19. What is the sum of
all four of Cleo's favorite numbers?

Answer 1

Based on the given conditions, formulate: 64/4

Answer 2

Answer: 21

Step-by-step explanation: First, you give the four numbers their own variables. Then, because 3 of them add to one number, you do a+b+c=13, b+c+d=14, c+d+a=17, and d+a+b=19. Because a+b+c=13 and d+b+c=14, d=a+1. Because a+b+c=13 and a+b+d=19, d=c+6. Because a+b+c=13 and a+d+c=17, d=b+4. You can also say that a=d-1, b=d-4, and c=d-6. If you use substitution on the first equation, we get (d-1)+(d-4)+(d-6)=13. If you simplify it, you get d=8, meaning a=7, b=4, and c=2. If you add 8+7+4+2, you get 21, which is the answer.